Cross-Cultural Analysis of Students with Exceptional Talent in Mathematical Problem Solving

A t a conference held in January 2005, Lawrence Summers, then president of Harvard University, hypothesized that a major reason for the paucity of women mathematicians among the tenured faculty of elite research universities in the USA might be sex-based differences in “intrinsic aptitude” for mathematics, especially at the very high end of the distribution [36]. This commonly held belief is largely based upon data from standardized tests such as the quantitative section of the Scholastic Aptitude Test (SAT) I. This test, designed to determine mathematical proficiency of USA eleventh and twelfth graders, identifies students who have mastered grade-level material, but does not distinguish the profoundly gifted, that is, those who are four or more standard deviations above the mean, from the merely gifted who also score in the ninety-ninth percentile on this exam. To identify students who perform above grade level, the Study of Mathematically Precocious Youth (SMPY) administered the SAT I to children younger than thirteen years of age. The SMPY defined children as highly gifted in mathematics if they scored at least 700 (on a 200 to 800 scale) on the quantitative section of this test. Using this criterion, Benbow and Stanley reported in 1980 large gender differences in “mathematical reasoning ability” [4]. They concluded that “sex differences in achievement in and attitude towards mathematics result from superior male mathematical ability . . . [it] is probably an expression of a combination of both endogenous and exogenous variables.” Since these tests lack questions that require creative thinking and insight into higher-level mathematical concepts, they do not identify children with extremely high innate ability in mathematics, that is, ones who may go on to become top research mathematicians. They cannot differentiate between profoundly and moderately gifted children, regardless of age at which the examinations are administered. Thus, the SMPY identified thousands of children who, while quite bright and ambitious, were not necessarily profoundly gifted in mathematics. The SMPY also failed to identify many children with extreme ability in mathematics who lacked one or more of the socio-economically privileged environmental factors necessary to be recognized by this mechanism. Coincidentally, the ratio of boys to girls identified in the SMPY has dramatically declined during the past quarter century from the high of 13:1 originally reported in 1983 [5] to 2.8:1 in a 2005 report [6]. The fact that 29% of Ph.D.’s awarded to USA citizens in the mathematical sciences went to women in the 2006–2007 academic year [30] supports the idea that this latter ratio is a more accurate reflection of current Titu Andreescu is professor of science/mathematics education at the University of Texas, Dallas. His email address is [email protected].